There are 3 US Post Offices in Owen County serving a total of 7,102 residents equating to 2,367 residents per post office. It's estimated that approximately 11,336 packages are handled across the 3 county post offices annually. Owen County is a county located in the U.S. state of Kentucky. As of the 2010 census, the population was 10,841. Its county seat is Owenton. The county is named for Colonel Abraham Owen. It is a prohibition or dry county, with the exception of a winery (Elk Creek Vineyards) that is authorized to sell its product to the public, and limited sales within the incorporated city limits of Owenton."